Circumradius Of Tri Equilateral Trapezoid Calculator

Circumradius of Tri-equilateral Trapezoid Formula:

\[ r_c = l_e \times \sqrt{\frac{l_e \times (l_u + l_e)}{4 \times l_e^2 - (l_u - l_e)^2}} \]

Circumradius (r_c):

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1. What is Circumradius of Tri-equilateral Trapezoid?

The circumradius of a tri-equilateral trapezoid is the radius of the circumcircle that passes through all four vertices of the trapezoid. A tri-equilateral trapezoid has three equal sides and one unequal side (typically the longer base).

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

\[ r_c = l_e \times \sqrt{\frac{l_e \times (l_u + l_e)}{4 \times l_e^2 - (l_u - l_e)^2}} \]

Where:

\( r_c \) — Circumradius of the trapezoid
\( l_e \) — Length of equal edge (three equal sides)
\( l_u \) — Length of unequal edge (the longer base)

Explanation: The formula calculates the radius of the circle that circumscribes the tri-equilateral trapezoid based on its side lengths.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry for understanding the properties of cyclic quadrilaterals, designing circular patterns, and solving problems related to inscribed figures in circles.

4. Using the Calculator

Tips: Enter the length of the equal edge and unequal edge in meters. Both values must be positive numbers, and the denominator in the formula must be positive for a valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a tri-equilateral trapezoid?
A: A tri-equilateral trapezoid is a trapezoid with three sides of equal length and one side (typically the longer base) of different length.

Q2: When is the circumradius calculation not possible?
A: The calculation requires that the denominator (4×l_e² - (l_u - l_e)²) be positive. If this value is zero or negative, the trapezoid cannot be circumscribed by a circle.

Q3: What are the units of measurement?
A: The calculator uses meters, but the formula works with any consistent unit of length (cm, mm, inches, etc.).

Q4: Can all trapezoids be circumscribed by a circle?
A: No, only cyclic quadrilaterals can be circumscribed by a circle. A trapezoid is cyclic if and only if it is isosceles.

Q5: How accurate is the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications.